Multi-Entity Bayesian Networks for Situation
E. Wright, S. Mahoney, K. Laskey, M. Takikawa, T. Levitt
Information Extraction & Transport, Inc.
1911 N. Ft Myer Drive, Suite 600, Arlington, VA 22209
Corresponding Author: firstname.lastname@example.org
Abstract - Reasoning about military situations requires a
scientifically sound and computationally robust
uncertainty calculus, a supporting inference engine that
procedurally encodes the axioms of the calculus, the
capability to fuse information at multiple levels of
abstraction, and the ability to respond to dynamic
situations. The inference engine also needs to be able to
encapsulate expert knowledge, including deep human
doctrinal and domain knowledge. At Information
Extraction & Transport, Inc. (IET), we have developed
techniques to encode domain and doctrinal expertise in
reusable knowledge chunks, based on the technology of
Bayesian Network Fragments, and the capability to
automatically construct situation specific Bayesian
Networks based on a combination of top down control and
bottom up evidence-driven processes. These techniques
have been used to prototype fusion systems capable of
reasoning about uncertain numbers of uncertain
hierarchically organized entities based on incomplete
observations. These systems have demonstrated success in
generating force level situation hypotheses from vehicle
tracks and other evidence generated by level 1 fusion
systems. This paper presents an overview of our technical
approach with applications from recent projects.
Keywords: Bayesian Networks, multi-entity Bayesian
Networks, situation assessment, hypothesis management
Military situation assessment requires reasoning about an
unknown number of hierarchically organized entities
interacting with each other in varied ways. The entities
are observed by various sensors, which generate sensor
reports or feed level 1 fusion systems that generate
estimates of various attributes of the entities. In general,
these reports cannot be unambiguously associated with the
domain entities generating them. For example, in ground
combat scenario, level 1 fusion systems generate a stream
of tracks, or tracklets, with likelihoods for vehicle types
and activities. This evidence stream is subject to errors –
including missed detections, false alarms, misassociation,
misclassification. This paper describes IET’s approach
for processing this kind of errorful evidence stream to
generate a situation assessment.
Section 2 provides an overview of the application of
Bayesian Networks (BNs) and Bayesian Network
Fragments (BNFrags) to information fusion, and
introduces our BN inference engine. Section 3 introduces
Multi-Entity Bayesian Networks (MEBNs), a
specialization of BNFrags. Section 4 introduces
hierarchical models for classification, and section 5
presents the technology of situation specific network
construction, hypothesis management, and evaluation.
Section 6 provides a summary of an example from a
recent research program.
2 Bayesian Networks for
A BN represents the probabilistic dependencies among a
set of random variables by a directed acyclic graph .
Each node in the network represents a random variable
with a set of defined states that together typically
represent a set of mutually exclusive and exhaustive
possible values for some hypothesis. A node in a BN is
conditionally independent of all non-descendant nodes
given its direct parents. Each node in the network stores
its probability distribution given its direct parents and any
evidence that has been observed concerning the node.
This information is sufficient to implicitly represent the
full joint probability distribution over all random variables
in the network, as well as the conditional joint distribution
given observed evidence about some nodes in the
The knowledge required to construct the BN can be
learned from existing data, can be defined by known
functional relationships, by elicitation from human
experts, or by any combination of the above.
2.1 Bayesian Network Fragments
The vast majority of published applications of BNs consist
of template models. A template model is appropriate for
problem domains in which the relevant variables, their
state spaces, and their probabilistic relationships do not
vary from problem instance to problem instance. Thus,
generic knowledge about the domain can be represented
by a fixed BN over a fixed set of variables, obtained by
some combination of expert judgment and learning from
observation. Problem solving for a particular case is
performed by conditioning the network on case-specific
evidence and computing the posterior distributions of
variables of interest.
For example, a medical diagnosis template network would
contain variables representing background information
about a patient, possible medical conditions the patient
might be experiencing, and clinical findings that might be
observed. The network encodes probabilistic relationships
among these variables. To perform diagnosis on a
particular patient, background information and findings
for the patient are entered as evidence and the posterior
probabilities of the possible medical conditions are
reported. Although values of the evidence variables vary
from patient to patient, the relevant variables and their
probabilistic relationships are assumed to be the same for
all patients. It is this assumption that justifies the use of
The development of efficient belief propagation
algorithms for template models enabled an explosion of
research and applications of probability models in
intelligent systems[1, 2]. As BN technology is applied to
more complex problems, the limitations of template
models become apparent. Even when a domain can be
represented by a template model, its size and complexity
may make it necessary to represent it implicitly as a
collection of modular subunits .
It is clear that a template model is inadequate for any type
of military situation assessment. The number of actors of
any given type is not static, but varies from situation to
situation. A reasoning system must be capable of unifying
reports with already-hypothesized units and/or
hypothesizing new units, as the context for the current
problem demands. The relevant variables for reasoning
about an actor depend on the actor’s type. For example,
the mode in which a radar emits is a key variable for
inferring the activity of a surface-to-air missile battery.
However, this variable is not applicable to units that have
no radar. Clearly, a network with a fixed set of variables
and a fixed topology is inadequate for this problem.
To address this issue, IET has pioneered research that
supports the decomposition of complex models into
conceptually meaningful and manageable pieces called
BNFrags . Opportunities for decomposition and reuse
occur when families of variables share the same sets of
possible values, when sets of related variables have a
common structure and when possible variables, values and
conditioning relationships can be parameterized.
Structural and parametric regularities also occur within
the conditioning distributions of BN. Network fragments
represent shared elements of a probabilistic knowledge
base. Each network fragment contains probabilistic
knowledge about a small set of random variables.
Moreover, a network fragment may represent only a
portion of a conditional probability distribution for a
variable given its parents. Model specification, model
maintenance, and communication are facilitated if models
are specified as network fragments.
Patterns of entity structure, behavior and relationships can
be encoded as fragments of BNs . A knowledge base
consisting of a set of BNFrags that encodes human
expertise and domain knowledge can provide the building
blocks for assembling a situation specific BN.
The ability to select and combine the right BNfrags to
build the appropriate BN for the specific inference
requires a powerful BN inferencing engine.
2.2 The IET Inference Engine
Over the last decade IET has continuously built and
improved the inferencing technology we use to model
complex, real world problems. Figure 1 shows the current
IET inferencing components.
Java Symbolic Probabilistic Inferencing (JSPI) Engine
is based on the IET’s SPI algorithm. It is one of only
two known general solution algorithms for BNs. In
contrast to the alternate “join tree” approach to inference
in BNs, SPI has the following two important
characteristics. First, SPI is query based. SPI extracts the
• JSPI Script: Scripting language for
JPF / JSPI
• JAVA Probabilistic Frames (JPF):
Capability to manipulate / reuse
• JAVA Symbolic Probabalistic
Inferrencing (JSPI): Propagate
Uncertainty In Bayesian Networks
Figure 1. IET Inference Engine Components
minimum subset of a BN that is necessary for each query,
minimizing the amount of computation required for
answering the query. This is important because the same
query can be repeated many times for different points
within the area of interest. Second, SPI has local
expressions, an extension of BNs, used to express local
structure within a node. Local expressions can be used to
instantiate many independence relationships including
independence of causal influences and context-specific
independence. SPI exploits these independence
relationships in addition to the conditional independences
inherent in BNs for efficient inference in large BNs. SPI
has successfully computed queries for large “bench mark”
BNs, which the join-tree inference algorithm is unable to
compute in reasonable time. In addition, SPI's query-
oriented approach allows for compilation of any
probabilistic query into an efficient and small procedural
code. Because both the memory and CPU requirement of
this generated code is fixed; it is readily usable in an
embedded and/or real-time environment.
JAVA Probabilistic Frames (JPF)
is a knowledge
representation language based on frames (a widely used
knowledge representation in Artificial Intelligence)
augmented in various ways to express uncertainties. In
addition to frame (class) abstractions organized by “is-a”
hierarchies inherited from the frame system, JPF supports
mechanisms to express uncertainties about the value of
variables, the reference to instances, the existence of
instances, and the type of instances. JPF allows for
expressing domain knowledge as pieces of BNs (or
network fragments) in a modular and compact way,
facilitating reuse. Instances of probabilistic frames are
created dynamically for each instance, allowing situation
specific probabilistic inference. The probabilistic
inference is done by JSPI using a BN created dynamically
from the current set of probabilistic frame instances. This
generation of BNs from JPF utilizes JSPI's local
expressions to exploit all types of independence
relationships to speed up the inference.
is an object-oriented scripting language
designed specifically for BN applications. It provides full
access to all the functions of JSPI and JPF. It can be used
to dynamically construct BNs, make situation-specific
queries, and define and replace software components on
the fly. In addition, the JSPI Script language can be run
interactively from a command line, or can be used via an
API from within a larger software system - allowing
automated control over construction and manipulation of
3 Multi-Entity Bayesian Networks
An MEBN is a collection of BNFrags that satisfy
consistency criteria such that the collection specifies a
probability distribution over attributes of and relationships
among a collection of interrelated entities. An MEBN
implicitly encodes a probability distribution over an
unbounded number of hypotheses. For any given problem,
only a finite subset of these hypotheses will be relevant. A
formal theory for MEBNs is under development .
MEBN logic extends standard BNs to allow the kind of
replication and combination needed to reason about
complex problems in which variable numbers of entities
interact in varying ways. Implicitly encodes a joint
probability distribution over object-level domain entities.
Augmented with an ontology for higher-order probability,
MEBN also implicitly specifies higher-order distributions
and supports learning. MEBN can serve as both object
language and meta-language. When extended to a Multi-
Entity Decision Graphs (MEDG), the approach also can
support trading off computation against accuracy and/or
utility for decision making and resource allocation.
MEBNs are to regular BNs what algebra is to arithmetic.
If all we have is arithmetic, to figure out how much carpet
to buy for an arbitrary room requires a huge table that lists
lengths, widths and the area corresponding to every
possible length and width (or an instruction to fill in the
blank by multiplication). With algebra we can write a
single equation a = l x w, and represent the table in one
Similarly, if all we have is BNs, and there are M months
of data with N variables per month, we must build a BN
with MxN nodes, and fill in identical arcs and local
probability distributions at each time step. With MEBNs,
we can write a single BNFrag relating the variables at
time t with the variables at time t+1 and say "repeat for all
t's." Similarly, we can relate a vehicle’s type to the type of
the unit it is a member of and say "repeat for all vehicles
in a unit, and then repeat for all units." Standard
implementations of BNs do not provide this capability.
4 Hierarchical Models
BNFrags and MEBNs provide the structure for building
the knowledge base. But the knowledge base must capture
knowledge about the problem domain. In a military
ground combat domain the knowledge is typically
organized hierarchically. To build the knowledge base we
define BNFrags that correspond to knowledge chunks at
different levels of the hierarchy. Then evidence, when it is
available, can be applied to the appropriate level of
abstraction. Links between BNfrags at different levels of
the hierarchy allow evidence at one level to support
inference at another level of abstraction.
Knowledge can be refined along two
Type – We will usually start with the
most specific target type for which the
initial detection provides adequate
evidence (e.g., tracked vehicle) and
refine further as additional information
is gathered. This refinement is
performed based on both the
information gathered so far and the
commander’s interests. For example, a
commander may not care about wheeled
vehicles, but be particularly concerned
about cross-country attacks from tracked
vehicles, and want very refined
classification on any tracked vehicle.
Activity Aspect – Activities can provide powerful
information about type, even in the absence of direct
observations of type. For example logistics vehicles often
operate alone on a closed loop between a supply depot and
a supported unit. Combat vehicles – and most types of
potential high value targets - do not exhibit this behavior.
The activity aspect also applies to the related activities of
individual entities. As an example, a HUMINT report
may provide information that the fuel truck for a mobile
missile launcher has just departed a supply depot. If
assessed as credible, this report could cue an activity
based query to an MTI database for possible combinations
of tracklets leaving the depot at the correct time. The
result of this query may lead to the fuel truck entity.
Tasking sensors to follow the fuel truck may lead to direct
observation of the mobile missile.
Activities also occur in hierarchies. The activities of the
individual vehicles in a platoon are related to the platoon’s
activities, which are in turn related to the company’s
activities. With a hierarchical activity model, it is
possible to infer the activities of higher level units from
observations on their members.
The type and activity hierarchies provide a powerful and
flexible way to represent doctrinal knowledge – about
organization of forces, and about organized activities that
military forces engage in.
This kind of a hierarchical knowledge representation, with
the capability to add additional BNFrags at the appropriate
level of the hierarchy allow us to apply a wide range of
evidence from diverse sources at multiple levels of
abstraction to our information fusion problem.
5 Situation Specific Bayesian Networks
MEBNs, a powerful inference engine, and a hierarchical
model of the problem domain are prerequisites for
building a system that will automatically construct
situation specific BNs.
To reason about specified target hypotheses given
evidence about a particular situation, an ordinary finite
BN, called a situation-specific network (SSN), is
constructed from a MEBN knowledge base. The SSN
construction process is initiated when clusters of
observations or reports trigger firing of a suggestor.
Suggestors are modules that use features of the situation
to determine which hypotheses need to be represented.
The suggestor triggers retrieval of relevant BNFrags.
Actual entities from the situation replace the variables in
After retrieval, the BNFrags are combined, possibly with
an already existing SSN, to create a current SSN. Next,
evidence is applied to the SSN and inferences are drawn
about the target hypotheses. Finally, decision nodes are
evaluated to determine what action needs to be taken. An
architecture for SSN construction is shown in Figure 2.
5.1 Automated Construction
Hypothesis management is the name of the capability we
embody in a software module that manages the
composition of the constructed system model. It includes
suggestors, described above, as well as rules for pruning
hypotheses. Hypotheses management is an important part
of the domain knowledge base. Mission parameters
establish the decisions to be made and the type of
available evidence (e.g. sensor data). The specified
decisions determine the relevance of elements of available
evidence. Both the decisions and available evidence set
the scope for the entities of interest and relationships to be
included in the system model.
Individual suggestors examine relevant evidence and the
current state of the system model to suggest that new
hypotheses be instantiated. For reasons of efficiency,
individual suggestors are tailored to types of evidence and
the entities of interest about which inferences are to be
made. Consequently, the task of hypothesis management
into SSN &
Figure 2 High Level Architecture for SSN Construction from MEBN
meta-level reasoning is to select the suggestors that meet
the requirements established by the mission parameters.
Action level hypothesis management makes two types of
decisions. Construction suggestors make decisions about
what hypotheses to add to the constructed model.
Revision suggestors make decisions about what to
change within the model.
The JPF knowledge structures a suggestor may reason
about include the following :
Entities: whether an entity of interest exists. This is called
existence uncertainty. False alarms are non-existent
entities of interest.
Relationships among entities: which two entities out of
several possible pairing share a specified relationship.
This is called reference uncertainty. Associating evidence
with an object establishes a relationship. Reference
uncertainty applies when there is uncertainty about which
object actually caused the evidence.
Entity types: When an entity of interest is identified, it
may be of one or more possible subtypes. This is called
Variable resolution: The best partition of a variable's
possible values depends upon the requirements of the
situation and the granularity of the available data.
Dependency relation: We may want to
modify/adapt/replace one conditional relationship with
another as the context varies or we learn.
When reasoning about an entity of interest, hypothesis
management suggestors make decisions about
instantiating instances of the entity, removing instances of
the entity and revising entity instances. A suggestor may
decide to instantiate the entity as a hypothetical
(uncertain) instance. While the suggestor has some
information associated with an entity of interest, there is a
'reasonable' chance that this entity may be a false alarm. If
there is enough information, the suggestor may
recommend that the entity be instantiated as a certain one.
Alternatively, the suggestor may choose to not instantiate
the entity at this time because of insufficient information.
Other suggestors may decide to remove the entity from
the situation-specific network, decide to make a
hypothetical entity into a certain one, or decide to take no
action. Similar types of suggestors make reference
uncertainty decision. Subtyping suggestors follow the isa
relationship among entities. Variable resolution reasoning
requires suggestors guided by the mission parameters to
determine the granularity of the states of the variables.
Granularity roughly corresponds to discrimination power.
Whenever certain variables have known values, they
effectively minimize the size of the conditional
probability distributions. These are called context
variables. However, in the course of a mission, a context
variable may change or be found to be in error.
Hypothesis management suggestors need to respond to
that change and modify the conditional probability
distributions of the model accordingly.
An example software component that constructs SSNs is
the Tactical Site, Group, Unit, and activity Detection and
Assessment (TSGUDA) as it was used in the DARPA
Dynamic Data Base (DDB) program . This data
consisted of fused tracks produced by the All-source
Track and ID Fusion (ATIF) component, as well as MTI
flow data and SIGINT emissions density data. The first
functional component of TSGUDA is the “suggestors”.
They identify possible hypotheses which are passed to a
software module called the assessment engine, which
builds and maintains the SSN. The suggestors use the
available knowledge models, and the current hypotheses
maintained in the assessment engine. The role of the
suggestors is to detect, with a high probability of detection
(and corresponding high false alarm rate) many possible
candidate hypotheses from the data. Note that the
suggestors are part of the knowledge representation for the
problem domain. The suggestors determine how the data
is potentially relevant to the current SSN, and suggest the
addition of new BNFrags to the existing network. They
may also suggest the addition of new levels of the type or
The candidate hypotheses, generated by the suggestors,
are sent to the assessment engine, that is responsible for
building and maintaining the situation specific BN.
Hypotheses in the situation estimate are represented by
nodes, or collections of nodes, in the BN. The current BN
can be queried at any time to provide an assessment of
any hypotheses. The assessment engine is also capable of
performing hypotheses management, by periodically
evaluating all, or a specific subset of the probabilistic
hypotheses and either eliminating them or declaring them
to be true.
The situation specific BN is maintained by the assessment
engine. It changes dynamically over time, as suggestors
present new candidate hypotheses, and as the hypothesis
management functions prune the network. There is also a
capability to store the current state of the network in the
“frame cache”. This provides the capability to store the
history of the situation estimate as it evolves over time,
and a future capability to “backtrack” to an earlier state if
the system discovers that it is diverged too far from
To be of value, the results of Information fusion must be
credible to decision makers. This requires that there is a
way to evaluate the situation hypotheses that have been
In previous work [8, 9] we demonstrated the capability to
measure the fidelity of a situation estimate to ground truth,
at either a single or at multiple levels of a force hierarchy.
The elements evaluated include:
• Hypotheses about entities of interest and their
• An indication of which reports and/or lower level
situation elements are associated with each
hypothesized entity of interest;
• Inferences about features of the entities of
Relevant features may include:
• Type of entity (e.g., maneuver company, engineer
• Location of entity;
• Composition of entity (e.g., number of elements of
• Activity of entity.
Evaluating the quality of a situation estimate in
comparison with a ground truth scenario requires first
associating situation hypotheses with the ground truth
elements that gave rise to them and then evaluating how
well the situation hypotheses represent the ground truth
elements that they represent. In particular, a situation
estimate is a faithful representation of a ground truth
scenario to the extent that:
• Most ground truth elements are associated with
situation hypotheses (there are few missed
• Most situation hypotheses have exactly one ground
truth element associated with them (there are few
• The features of interest (e.g., type, location,
composition, activity) of the ground truth element are
faithfully represented in the situation hypothesis.
Sit Est to GT
Confidence Vs Fidelity
• With variety of scenarios, vary random variables that
characterize input data quality, to statistically evaluate
performance of the system model.
• Situation estimate results are compared to Ground Truth to
• Estimated confidence is compared to fidelity scores to evaluate
the systems ability to predict its own accuracy
Figure 3. Experimental architecture.
The ability to generate a situation estimate has little value
unless there is some confidence that the estimate is
accurate enough to be useful to a decision maker. An
evaluation can be done subjectively by visually comparing
a situation estimate with known ground truth. But a
subjective evaluation is time consuming to perform and is
of little value in quantifying the effects of small changes
in domain models, suggestor logic, or hypothesis
management. In addition, there are usually only a limited
number of ground truth data sets available. Based on
similar concerns in other problem domains we have
developed an experimental architecture that allows us to
systematically evaluate a system model and its
components. The experimental architecture is shown in
Because of the limited real world ground truth, and the
need to evaluate system model performance against a
variety of scenarios, evaluations were performed with
simulated scenarios. The simulations defined the types,
membership, and activities of a hierarchy of military units,
and then generate each specific vehicle track. The vehicle
tracks were then processed to simulate the TSGUDA
inputs, normally received from the ATIF system. The
processing may be “error free” to provide ground truth
data to TSGUDA, or it may simulate the types of errors
characteristic of real TSGUDA input data. We
implemented error models for probability of vehicle type
ID, probability of detection, probability of correct
association (of a vehicle track at one time step with the
correct track at the next time step), and a false alarm rate.
The simulated ground truth, with simulated error models
applied, was then input to the system model, which
generated situation estimates over time as the situation
developed. These situation estimates were compared to
the original ground truth situation to generate a fidelity
score. The fidelity scoring process is described in .
The results of the fidelity score can be used in a feedback
process to tune the models, suggestor logic, and
hypothesis management logic.
It is understood that a fidelity measure can only be used
when ground truth is available, so will be of no use in a
real military situation where a TSGUDA like situation
estimation capability is needed. Figure 3 also shows a
confidence calculation. The confidence measure is a
metric developed by the system based on the quantity and
believed quality of the input data, consistency between the
available evidence, and the fit to existing models. The
confidence measure will provide an estimate of the quality
of the situation estimate independent of ground truth. The
theory for the confidence calculation has been developed
, and implementation is in progress.
An example that illustrates the ability to recognize a
military force hierarchy as part of a situation assessment
Score (Ave Loss): 122
Force Level Hypotheses 1
Score (Ave Loss): 223
Force Level Hypotheses 2
Figure 4. Ground truth force level hypotheses with two example situation hypotheses.
in Figure 4. The assessment was performed using
TSGUDA with simulated data. The ground truth force
hierarchy is shown consisting of a Armor Heavy
Company Team, with a HQs Plt, two Armor Platoons, and
a Mechanized Infantry Platoon. A simulated scenario that
included coordinated activities of these units was used to
generate ground truth tracks for all the individual vehicles.
Then a level 1 fusion simulator was used to generate
vehicle tracks. These observed tracks included
missed detections, false alarms, track misassociations and
type misclassifications. This evidence was input to the
TSGUDA system. There is also a separate Engineer
The TSGUDA system included domain models for
platoon an company level force organization and
activities. Suggestors looked for clusters of vehicles and
hypothesized that they were groups. Other suggestors
looked at the evidence for vehicle types in a hypothesized
group, and suggested group, or unit, types. Additional
suggestors identified clusters of platoons to hypothesize
company sized groups, and assessed platoon type
hypotheses to suggest the company type. In addition,
other suggestors, evaluated the locations of individual
vehicles to suggest possible platoon formations, which
combined with activities of individual vehicles, suggested
Two example force level hypotheses, generated from two
different sets of simulated level 1 fusion inputs, are also
shown. In the first, the simulated level 1 fusion errors
were consistent with the performance of the ATIF system.
In this example all platoons have been detected and
identified with high probabilities. The differences between
the ground truth and the hypotheses is in the hypothesized
membership of the Engineer Platoon in the Company, and
in the vehicles hypothesized as members of the Engineer
Platoon (not shown). The score (average loss from the
fidelity scoring algorithm) is 122.
The second force level hypotheses was generated from a
simulation with significantly higher simulated level 1
fusion errors. This set of hypotheses contains a company
of unknown type, consisting of three platoons of unknown
type, and one additional platoon. The separate Engineer
platoon was not detected in this example. The score
(average loss from the fidelity scoring algorithm) for this
example is 223. While these results are poorer then the
first example, they do demonstrate that our approach for
situation assessment can identify force hierarchies, even in
the presence of significant input errors.
This paper has outlined the IET approach to situation
assessment. Our key tenets are
i) that hiearchical Bayesian inference as embodied in
BNs provide a scientifically sound and robust
ii) the SPI algorithm provides the necessary solution
modularity to drive dynamic situation assessment;
iii) that human expertise and domain knowledge can be
captured in hierarchical models of the task domain;
iv) the knowledge can be represented in modular and
parametrizable BNFrags and MEBNs;
v) robust decision logic can be designed to guide the
construction of situation specific BNs;
vi) there are practical methodologies to evaluate the
fidelity of assessment;
vii) together, these elements provide a demonstrated
capability to perform information fusion for
dynamic, scalable situation assessment.
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